Adding AUC statistical significance routines (sAUC,sAUCapparox,sAUC2)

NAMESPACE

@@ -7,4 +7,7 @@ export(setEventTime)
 export(simple.compute_roc_metrics)
 export(simple.getAUC)
 export(simple.roc)
+export(simple.sAUC)
+export(simple.sAUC2)
+export(simple.sAUCapprox)
 export(sumWithNA)

R/roc.R

@@ -105,3 +105,93 @@ simple.compute_roc_metrics <- function(ROC) {
   ))
 }
 
+#' Calculate covariance of AUC (deLonghi)
+#'
+#' @param roc roc as calculated by simple.roc
+#'
+#' @return standard deviation of AUC
+#'
+#' @export
+
+simple.sAUC <- function(roc) {
+  V1 = roc[roc$labels, 'V']
+  AUC = base::mean(V1)
+  V0 = roc[!roc$labels, 'V']
+  n0 = base::length(V0)
+  n1 = base::length(V1)
+
+  S0 = base::sum((V0 - AUC) * (V0 - AUC)) / (n0 - 1)
+  S1 = base::sum((V1 - AUC) * (V1 - AUC)) / (n1 - 1)
+  base::sqrt(S0 / n0 + S1 / n1)
+}
+
+#' Calculate covariance of AUC (approximation)
+#'
+#' @param roc roc as calculated by simple.roc
+#'
+#' @return standard deviation of AUC
+#'
+#' @export
+
+simple.sAUCapprox <- function(roc) {
+  n = base::length(roc$labels)
+  auc = simple.getAUC(roc)
+  auc_se = base::sqrt((auc * (1 - auc) + (n - 1) * (auc - 0.5)^2) / n)
+  auc_se
+}
+
+#' Check whether two AUCs are statistically significantly different
+#'
+#' @param rocA roc of the first test as returned by simple.roc
+#' @param rocB roc of the second test as returned by simple.roc
+#'
+#' @return p of the test
+#'
+#' @export
+
+simple.sAUC2<-function(rocA,rocB){
+   #NCSS
+   #https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Comparing_Two_ROC_Curves-Paired_Design.pdf
+   #calculate combined variance of two predictions on the same dataset
+   #and give p-value that their performance is the same (or, with low p, that it is different)
+   V0A=rocA[!rocB$labels,'V']
+   V0B=rocB[!rocB$labels,'V']
+   V1A=rocA[rocA$labels,'V']
+   V1B=rocB[rocB$labels,'V']
+   AUCA=base::mean(V0A)
+   AUCB=base::mean(V0B)
+   n0=base::length(V0A)#the same as V0B
+   n1=base::length(V1A)#the same as V1B
+   base::print(base::sprintf('A=%f B=%f',AUCA,AUCB))
+   #variance of the 0 component, A
+   S0A=base::sum((V0A-AUCA)*(V0A-AUCA))/(n0-1)
+   #variance of 1 component, A
+   S1A=base::sum((V1A-AUCA)*(V1A-AUCA))/(n1-1)
+   #variance of A
+   SA=S0A/n0+S1A/n1
+   #variance of the 0 component, B
+   S0B=base::sum((V0B-AUCB)*(V0B-AUCB))/(n0-1)
+   #variance of 1 component, B
+   S1B=base::sum((V1B-AUCB)*(V1B-AUCB))/(n1-1)
+   #variance of B
+   SB=S0B/n0+S1B/n1
+   #covariance 0 component
+   S0AB=base::sum((V0A-AUCA)*(V0B-AUCB))/(n0-1)
+   #covariance 1 component
+   S1AB=base::sum((V1A-AUCA)*(V1B-AUCB))/(n1-1)
+   #covariance
+   SAB=S0AB/n0+S1AB/n1
+   S=SA+SB-2*SAB
+   #is there a significant difference
+   z=base::abs(AUCA-AUCB)/base::sqrt(S)
+   p=2*stats::pnorm(z,mean=0,sd=1,lower.tail=FALSE)
+
+   #is A larger than B
+   #z=(AUCA-AUCB)/sqrt(S)
+   #p=pnorm(z,mean=0,sd=1,lower.tail=FALSE)
+
+   base::print(base::sprintf('SA2=%f SB2=%f SAB2=%f S2=%f S=%f z=%f p=%f',SA,SB,SAB,S,base::sqrt(S),z,p))
+   p
+
+}
+

man/simple.sAUC.Rd

@@ -0,0 +1,17 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/roc.R
+\name{simple.sAUC}
+\alias{simple.sAUC}
+\title{Calculate covariance of AUC (deLonghi)}
+\usage{
+simple.sAUC(roc)
+}
+\arguments{
+\item{roc}{roc as calculated by simple.roc}
+}
+\value{
+standard deviation of AUC
+}
+\description{
+Calculate covariance of AUC (deLonghi)
+}

man/simple.sAUC2.Rd

@@ -0,0 +1,19 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/roc.R
+\name{simple.sAUC2}
+\alias{simple.sAUC2}
+\title{Check whether two AUCs are statistically significantly different}
+\usage{
+simple.sAUC2(rocA, rocB)
+}
+\arguments{
+\item{rocA}{roc of the first test as returned by simple.roc}
+
+\item{rocB}{roc of the second test as returned by simple.roc}
+}
+\value{
+p of the test
+}
+\description{
+Check whether two AUCs are statistically significantly different
+}

man/simple.sAUCapprox.Rd

@@ -0,0 +1,17 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/roc.R
+\name{simple.sAUCapprox}
+\alias{simple.sAUCapprox}
+\title{Calculate covariance of AUC (approximation)}
+\usage{
+simple.sAUCapprox(roc)
+}
+\arguments{
+\item{roc}{roc as calculated by simple.roc}
+}
+\value{
+standard deviation of AUC
+}
+\description{
+Calculate covariance of AUC (approximation)
+}